Mouse click fails to copy and keyboard selection loses window focus

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OS: Ubuntu 25.10, GNOME 49
Launch key: Menu, Shift+Ctrl+Space

How to reproduce:

1. Enable search for gnome-characters (System Settings → Search → Toggle on "Characters").
2. Invoke the extension.
3. Search for any character or emoji (e.g., "Green Apple").

Bug 1: Mouse selection fails

Clicking on a character with the mouse cursor does not copy it to the clipboard at all.

Bug 2: Keyboard selection focus issue

Copying via the keyboard works (Arrow Down → Enter), and the search bar disappears as expected. However, the focus does not return to the active application. You must manually press Esc or click the window to regain focus before you can type or paste.

Note: this also reproduces when I try to copy Calculator results.

Expected behavior:
The character should be copied via either a mouse click or keyboard selection (Enter). Once selected, the menu should disappear and focus should automatically return to the previous application so the character can be pasted immediately using Ctrl+V.